Mystery ruler
a l l y
objects each week... can you help me with my puzzling 6-inch ruler please?
It's been kicking about my house most of my life, but no-one has ever been
able to explain to me what the markings on the back are all about. You can
see it here: http://www.flickr.com/photos/allybeag/523961497/
Thanks!
ally
Robert Israel
I don't know what "Cho" is, but the markings on the back allow measurements
(in principle) to a precision of 1/100 or 1/200 inch. Thus to measure 1.46
inches, you go from the vertical line labelled 1 at the top to the slanted
line labelled 4 at the top, along the horizontal line labelled 6. The
slanted lines on the left allow measurements in 200ths of an inch.
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
a l l y
"Robert Israel" <isr...@math.MyUniversitysInitials.ca> wrote in message
news:rbisrael.20070531234150$76...@news.ks.uiuc.edu...
> "a l l y" <al...@situponDOGGIEseats.co.uk> writes:
>
>> So many clever people here! You're so good at identifying those mystery
>> objects each week... can you help me with my puzzling 6-inch ruler
>> please?
>> It's been kicking about my house most of my life, but no-one has ever
>> been
>> able to explain to me what the markings on the back are all about. You
>> can
>> see it here: http://www.flickr.com/photos/allybeag/523961497/
>
> I don't know what "Cho" is, but the markings on the back allow
> measurements
> (in principle) to a precision of 1/100 or 1/200 inch. Thus to measure
> 1.46
> inches, you go from the vertical line labelled 1 at the top to the slanted
> line labelled 4 at the top, along the horizontal line labelled 6. The
> slanted lines on the left allow measurements in 200ths of an inch.
> --
ally
mensa...@aol.com
Looks like a small Gunter's Scale (CHO stands for chord).
Used with dividers in navigation.
See
Mark Brader
And what exactly does "chord" mean here? Neither the site you cited nor
Wikipedia's article on Edmund Gunter appears to say. From the context
it would appear to be ome mathematical function of one argument, like
logarithms and trig functions, but I'm not aware of one by that name,
and Mathworld's article on "chord" doesn't mention one.
It's particularly interesting in that the chord scale is almost linear,
but not quite. I'm not aware of any commonly used function with that
characteristic over most of its useful range.
--
Mark Brader "I used to own a mind like a steel trap.
Toronto Perhaps if I'd specified a brass one, it
m...@vex.net wouldn't have rusted like this." --Greg Goss
My text in this article is in the public domain.
mensa...@aol.com
> > Looks like a small Gunter's Scale (CHO stands for chord).
>
> And what exactly does "chord" mean here?
Who knows? One site mentioned that Gunter scales were used up to
the 19th century, so maybe there's no one alive who's ever used one.
Here <http://www.sliderules.info/collection/nonstandard/023-
gunter.htm>
it's speculated degrees. For that matter, what's a "rhumb"? Anything
to
do with 15 men on a dead man's chest?
> Neither the site you cited nor
> Wikipedia's article on Edmund Gunter appears to say. From the context
> it would appear to be ome mathematical function of one argument, like
> logarithms and trig functions, but I'm not aware of one by that name,
> and Mathworld's article on "chord" doesn't mention one.
But this is interesting
<http://artematrix.org/computer.collection/gunters.scale.htm>
<quote>
The trig functions are defined in an equivalent, but different way,
then they are usually defined today; as lengths of lines rather
than ratios of lengths of lines.
</quote>
So you probably won't find correct info on MathWorld or Wikipedia.
Mike Williams
>
>And what exactly does "chord" mean here? Neither the site you cited nor
>Wikipedia's article on Edmund Gunter appears to say.
Doing a bit of reverse mathematical engineering, I reckon that you'd
have to know in advance that it's designed to work with a circle with a
six inch diameter. Perhaps you're supposed to guess that from the fact
that it's a six inch ruler.
Given two points on that circle, measure the length of the straight line
between them, the "chord", using the CHO scale. The number on the CHO
scale gives you the angle between those points in degrees.
For two points at 90 degrees, we can use Pythagoras to determine the
length to be sqrt(2*r^2). When r=3 inches the 90-degree chord is 4.24264
inches, which matches the length of the CHO scale. (Which is where I got
the "six inch diameter" from.)
Because the CHO scale isn't on the edge of the ruler, you can't measure
the length directly with the ruler. You have to use dividers to transfer
CHO lengths to and from the ruler. Perhaps this rather cumbersome method
of measuring angles might produce slightly more accurate results than
using a small protractor.
--
Mike Williams
Gentleman of Leisure
mike3
> On May 31, 10:38?pm, m...@vex.net (Mark Brader) wrote:
<snip>
For that matter, what's a "rhumb"? Anything
> to
> do with 15 men on a dead man's chest?
>
I think that a "rhumb" is a point on the compass rose, as in a rhumb
line, or loxodromic route between two points on the Earth's
surface (or any other sphere with a north-south axis), which is
a line of constant compass direction, ie. of constant "rhumb",
hence "rhumb line". This type of course is not the shortest
course on the sphere, however. The shrotest course across
the surface of the sphere is called an orthodromic, or great
circle, course and does not have a constant compass direction.
According to this page:
http://jacq.istos.com.au/sundry/navrhumb.html
a "rhumb" is
"...angle measurement representing the "point" on the old fashioned
compass cards. There are 32 "rhumbs" in 360 degrees, hence a
rhumb is 11 1/4 degrees. "
The site talk baout the thing having a possible use in navigation,
hence
"rhumbs".
And by the way, a "chord" is the line segment between two points
on a curve.
a l l y
most of my life and now I've got loads of fascinating information to mull
over. I wonder if it's somewhat older than I supposed, then? When I was at
primary school my parents let me use it as a nice neat little school ruler
that fitted into my pencil case, and I sort of assumed it was new then, but
given that I am not older than the invention of the slide rule, I guess
that's not the case! We did have several ancestors who went to sea, so
perhaps it belonged to one of them.
ally
Phil Carmody
Oh how little imagination people have nowadays!
It helps you measure hundredths of inches. If you
have something just over 1.2 inches long (say 1.23),
then position it at the 1 inch marker (roughly in
the middle of the picture), and slide it down until
the diagonal starting at tick 2 matches exactly
your objects length. That will be on the third row
down, and from that you deduce the length is 1.23.
The diagonals at the left appear to permit measurement
to 1/200" precision.
And for reference, I've never seen such a ruler before,
it just appeared obvious that it's a type of vernier
scale.
Phil
--
"Home taping is killing big business profits. We left this side blank
so you can help." -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
Phil Carmody
> > Looks like a small Gunter's Scale (CHO stands for chord).
>
> And what exactly does "chord" mean here? Neither the site you cited nor
> Wikipedia's article on Edmund Gunter appears to say. From the context
> it would appear to be ome mathematical function of one argument, like
> logarithms and trig functions, but I'm not aware of one by that name,
> and Mathworld's article on "chord" doesn't mention one.
>
> It's particularly interesting in that the chord scale is almost linear,
> but not quite. I'm not aware of any commonly used function with that
> characteristic over most of its useful range.
So you're not aware of trigonometric functions?
The way that the scale shrinks as the values increase,
it might map a chord length onto a subtended angle.
However, that's not a scale-invariant mapping, it would
only work for one radius.
a l l y
"Phil Carmody" <thefatphi...@yahoo.co.uk> wrote in message
news:87myzk6...@nonospaz.fatphil.org...
> "a l l y" <al...@situponDOGGIEseats.co.uk> writes:
>> So many clever people here! You're so good at identifying those mystery
>> objects each week... can you help me with my puzzling 6-inch ruler
>> please?
>> It's been kicking about my house most of my life, but no-one has ever
>> been
>> able to explain to me what the markings on the back are all about. You
>> can
>> see it here: http://www.flickr.com/photos/allybeag/523961497/
>
> Oh how little imagination people have nowadays!
Hey, we're not all mathematicians you know! My artisitic and musical
imaginations are working just fine though.
;-)
>
> It helps you measure hundredths of inches. If you
> have something just over 1.2 inches long (say 1.23),
> then position it at the 1 inch marker (roughly in
> the middle of the picture), and slide it down until
> the diagonal starting at tick 2 matches exactly
> your objects length. That will be on the third row
> down, and from that you deduce the length is 1.23.
>
> The diagonals at the left appear to permit measurement
> to 1/200" precision.
Thanks.
I'd almost worked it out as far as that, but couldn't quite see how it was
done. My gut feeling was that it was a sort of pre-slide-rule thing, so as a
non-mathematician I wasn't that far off the mark, was I?
ally
Mark Brader
> Doing a bit of reverse mathematical engineering, I reckon that you'd
> have to know in advance that it's designed to work with a circle with a
> six inch diameter. Perhaps you're supposed to guess that from the fact
> that it's a six inch ruler.
>
> Given two points on that circle, measure the length of the straight line
> between them, the "chord", using the CHO scale. The number on the CHO
> scale gives you the angle between those points in degrees.
Aha! Thanks, well solved -- it's obvious *after* you point it out!
I should have realized that "chord" suggested circles and in that
context the fact that the scale went to 90 might imply degrees.
So, if you had three points ABC marked on a chart and you wanted to
measure angle ABC, you drew the lines AB and BC, set your compass
to a radius of 3 inches, drew an arc with center B crossing both
lines, and then measured it with the CHO scale. Considering the
possible inaccuracies at each stage, it doesn't sound like a very
good technique.
Also, what if the angle is more than 90 degrees? (Thinks a moment.)
Right, then you simply extend one of the lines past B, measure the
supplementary angle, and subtract from 180.
And... Aha! Perhaps it is a good technique if the reason you don't
have available a protractor as we know them is that *transparent plastic
has not yet been invented*. A protractor made out of wood or metal
would need a hole or notch at the vertex of the angle, and might be
hard to place accurately. And a glass one would be easy to break.
--
Mark Brader, Toronto | "We don't use clubs; they weren't invented here.
m...@vex.net | We use rocks." -- David Keldsen
mensa...@aol.com
It was a joke.
Yo, ho, ho and a bottle of rhumb. Get it? :-)
I kinda knew what "rhumb" was as regards to a Mercator
projection and lines of constant compass bearing, not
the compass points though.
My dad was an LCI captain in WWII and I have a dim memory
of drawing with his navigation tools as a kid. The only
one I remember was the pair of rulers with connecting
braces for drawing parallel lines.
Mark Brader
> > It's particularly interesting in that the chord scale is almost linear,
> > but not quite. I'm not aware of any commonly used function with that
> > characteristic over most of its useful range.
> So you're not aware of trigonometric functions?
They don't meet that description.
> The way that the scale shrinks as the values increase,
> it might map a chord length onto a subtended angle.
> However, that's not a scale-invariant mapping, it would
> only work for one radius.
So it seems.
--
Mark Brader "If Benjamin Franklin was alive today, he'd be
Toronto arrested for sailing a kite without a license."
m...@vex.net -- Tucker: The Man and his Dream
Phil Carmody
> Mark Brader:
> > > It's particularly interesting in that the chord scale is almost linear,
> > > but not quite. I'm not aware of any commonly used function with that
> > > characteristic over most of its useful range.
>
> Phil Carmody:
> > So you're not aware of trigonometric functions?
>
> They don't meet that description.
All of them?